Statistical structures on tangent bundles and Lie groupps

Let TM be a tangent bundle over a Riemannian manifold M with a Riemannian metric g and TG be a tangent Lie group over a Lie group with a left-invariant metric g. The purpose of the paper is two folds. Firstly, we study statistical structures on the tangent bundle TM equipped with two Riemannian g-natural metrics and lift connections. Secondly, we define a left-invariant complete lift connection on the tangent Lie group TG equipped with metric ge introduced in [F. Asgari and H. R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo II. Series, 2018] and study statistical structures in this setting.